A 3-D discrete element model with connective type was presented in this paper. Accordingly, a 3-D discrete element method code, which can calculate the transitional process from connective model (for continuum) to contact model (for non-continuum), was developed. The wave propagation in a 3-D concrete block under impact loading was numerically simulated, by using this code. Comparing its numerical results with those by LS-DYNA, the accuracy of this algorithm was presented. Moreover, the failure process of the concrete block under impact loading was demonstrated, which presented the basic dynamic transitional process from continuum to non-continuum. The two numerical examples prove that the new model and its code are powerful and efficient for simulating the dynamic failure problems accompanying with the transition from continuum to non-continuum. It also shows that the discrete element method will have widespread availability and perfect development prospect.